Question: 89: Copper crystallises in fcc unit cell with cell edge length of 3.608 \times 10^{-8} \mathrm{~cm}. The density of copper is 8.92 \mathrm{~g} \mathrm{~cm}^{-3}. Calculate the atomic mass of copper.
(1) 60 \, u
(2) 65 \, u
(3) 63.1 u
(4) 31.55 u
Answer: Option (3)
Explanation:
Copper crystallises in a face centred cubic (fcc) unit cell, for which the number of atoms per unit cell is Z=4.
The relation between density, atomic mass and unit cell parameters is given by
\rho=\frac{Z M}{a^{3} N_A}Rearranging the equation to calculate atomic mass M,
M=\frac{\rho a^{3} N_A}{Z}Given \rho=8.92 \, \mathrm{g\,cm^{-3}} and a=3.608 \times 10^{-8} \, \mathrm{cm}.
First calculate the volume of the unit cell:
a^{3}=(3.608 \times 10^{-8})^{3}=4.699 \times 10^{-23} \, \mathrm{cm^{3}}Substituting the values,
M=\frac{8.92 \times 4.699 \times 10^{-23} \times 6.022 \times 10^{23}}{4} M=\frac{252.4}{4} M=63.1 \, \mathrm{u}Therefore, the atomic mass of copper is 63.1 \, u.